SOLUTION: A box has the dimensions of 2 inches by 3 inches by 4 inches. Determine the approximate angle formed by the diagonal of the 2 X 3 side and the diagonal of the 3 X 4 side to the nea

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Question 389458: A box has the dimensions of 2 inches by 3 inches by 4 inches. Determine the approximate angle formed by the diagonal of the 2 X 3 side and the diagonal of the 3 X 4 side to the nearest degree?
Answer by robertb(5830) About Me  (Show Source):
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Let the length of the base be 4 inches, the width of the base be 3 inches, and the height, 2 inches. Then the measure of the diagonal of the 2x 3 face is sqrt%2813%29, the measure of the diagonal of the 3x 4 face is 5, and the measure of the diagonal of the 2x 4 face is 2sqrt%285%29. The three diagonals form a triangle. Then from the cosine law,
20+=+25+%2B+13+-+2%2A5%2Asqrt%2813%29%2Acos%28theta%29
===>+-18+=+-10sqrt%2813%29cos%28theta%29
===>cos%28theta%29+=+%289sqrt%2813%29%29%2F65
===> theta+=+60degrees, to the nearest degree.